A senior Indian government minister predicted upcoming state elections would be a “complete sweep” for Prime Minister Narendra Modi’s party, which is hoping that a strong mandate will help it push through more policy changes in the second half of Mr. Modi’s term.

Piyush Goyal, the power minister and an influential leader in the Bharatiya Janata Party, said he was comfortable using the term “sweep”—“I wouldn't use it in the normal course”—because of the depth of support he said he's seen for Mr. Modi’s radical move, in November, to invalidate all large bank notes as a way of punishing corrupt officials and tax evaders.

“His popularity has shot through the roof,” Mr. Goyal said in an interview with The Wall Street Journal. He said Mr. Modi wasn’t even this popular in 2014, the year in which the BJP won by a landslide in elections for Parliament’s lower house.

Winning this spring’s state contests would help the BJP increase its presence in the legislature’s upper house, where opposition parties have blocked some of Mr. Modi’s proposals. The polls are also the first major test of Mr. Modi’s popularity since the currency nullification, which left many Indians scrambling for cash for weeks. Results are due March 11.

Among the five states that will elect new governments is Uttar Pradesh, home to one in six Indians. There the BJP is gearing up for a tough fight against three rival parties, including two regional players that have long held power. Mr. Modi’s party hasn’t ruled the state in 15 years. It won a vast majority of the state’s parliamentary constituencies in the 2014 national election, though.

In the neighboring state of Bihar, the BJP in 2015 lost the assembly election to a coalition of regional rivals despite dozens of rallies addressed by the prime minister.

India Today, a news organization, said this month that a survey it commissioned predicted a BJP majority in Uttar Pradesh. Opinion polls in India have a spotty record at anticipating election outcomes, though.